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04 Feb 2006, 14:50
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If the interger n is greater than 1, is n euqal to 2?
1) n has exactly two positive factors
2) the difference of any two distinct positive factor of n is odd
1) n has exactly two positive factors
2) the difference of any two distinct positive factor of n is odd
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04 Feb 2006, 15:17
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(1) n has exactly two positive factors ==> n = prime, but n = 2, 3, 5, 7....Insufficient.
(2) the difference of any two distinct positive factor or n is odd ==>
Let n = 2, factors are 1 and 2, difference = 1.
Let n = 3, factors are 3 and 1, difference = 2.
Let n = 6, factors are 1, 2, 3, 6, difference of any two positive factor could be odd or even.
Thus any n>2 ==> difference of any two distinct positive factors of n will either be odd or even. n must equal to 2.
(1) n has exactly two positive factors ==> n = prime, but n = 2, 3, 5, 7....Insufficient.
(2) the difference of any two distinct positive factor or n is odd ==>
Let n = 2, factors are 1 and 2, difference = 1.
Let n = 3, factors are 3 and 1, difference = 2.
Let n = 6, factors are 1, 2, 3, 6, difference of any two positive factor could be odd or even.
Thus any n>2 ==> difference of any two distinct positive factors of n will either be odd or even. n must equal to 2.
I'm falling asleep......LOL 
